However, sampling in the \((L,A)\)  space (with each sample as the input to (REF ) with pre-defined initial condition, say \(\xi (0)=0\)  and \(\dot{\xi }(0)=0\)  as in [1]}, [2]}) loses critical information associated with \(\eta (t)\) . The most important one among them is the varying initial condition of the ship at the encounter of each wave group. As shown in [3]}, [4]}, (REF ) (and the ship roll in general) may be sensitive to the initial conditions for some \(A\)  and \(L\)  (see figure REF  as an example). This creates heteroscedastic uncertainty in the ItR (associated with \(\omega \) ) that needs to be dealt with by our current approach Seq-VHGPR.
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